PTCB Math Practice Test: 40 Free Questions With Worked Answers
Forty original, unofficial calculation questions written to PTCB's current PTCE content outline (effective January 6, 2026). Use a calculator, since the real exam has one built in, and open the worked solution under each question. Drug names add realism; the doses are math exercises, not dosing guidance.
Practice questions
Questions 1–7: Sig codes, quantity, and days supply
Question 1 of 40 · Days supply
M01. A prescription reads: metformin 500 mg tablets, take 1 tablet by mouth bid, #60. What is the days supply?
- A. 60 days
- B. 30 days
- C. 120 days
- D. 15 days
Show answer and worked solution
Answer: B — 30 days.
The sig code bid means twice a day, so the patient uses 2 tablets a day. Days supply = quantity ÷ daily use = 60 ÷ 2 = 30 days.
Why not the others: A treats one tablet as a full day's use. C multiplies instead of dividing. D divides by 4, which would be qid (four times a day).
PTCB outline area 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 2 of 40 · Quantity to dispense
M02. Gabapentin 300 mg capsules: take 1 capsule by mouth q8h. How many capsules are needed for a 30-day supply?
- A. 30
- B. 60
- C. 240
- D. 90
Show answer and worked solution
Answer: D — 90 capsules.
The sig code q8h means every 8 hours. 24 ÷ 8 = 3 doses a day, and 3 × 30 days = 90 capsules.
Why not the others: A is once daily and B is twice daily. C reads q8h as 8 doses a day.
PTCB outline area 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 3 of 40 · Taper quantity
M03. Prednisone 10 mg tablets. Directions: 40 mg daily for 3 days, then 30 mg daily for 3 days, then 20 mg daily for 3 days, then 10 mg daily for 3 days, then stop. How many tablets should be dispensed?
- A. 30
- B. 12
- C. 10
- D. 40
Show answer and worked solution
Answer: A — 30 tablets.
Turn each step into tablets first: 40 mg = 4 tablets, 30 mg = 3, 20 mg = 2, 10 mg = 1. Each step lasts 3 days, so (4 + 3 + 2 + 1) × 3 = 30 tablets.
Why not the others: B is the number of days, not tablets. C is one day of each step. D is the first step's daily milligrams, not a tablet count.
PTCB outline area 4.1, 1.4. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 4 of 40 · Liquid quantity
M04. Amoxicillin 400 mg/5 mL suspension: give 5 mL by mouth bid for 10 days. How many mL are needed to complete the course?
- A. 50 mL
- B. 75 mL
- C. 100 mL
- D. 150 mL
Show answer and worked solution
Answer: C — 100 mL.
5 mL × 2 doses a day = 10 mL a day, and 10 mL × 10 days = 100 mL.
Why not the others: A covers once-daily dosing. B is a common bottle size, not the calculated need. D assumes three doses a day.
PTCB outline area 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 5 of 40 · Eye drop days supply
M05. Timolol 0.5% ophthalmic solution, 5 mL bottle: instill 1 drop in each eye bid. For this question, assume the bottle delivers 20 drops per mL. (Drop size varies by product, so always use the figure you're given.) What is the days supply?
- A. 50 days
- B. 100 days
- C. 25 days
- D. 12 days
Show answer and worked solution
Answer: C — 25 days.
Total drops: 5 mL × 20 drops/mL = 100 drops. Daily use: 1 drop × 2 eyes × 2 times = 4 drops. 100 ÷ 4 = 25 days.
Why not the others: A forgets the second eye. B is the total number of drops. D uses 8 drops a day, doubling the real use.
PTCB outline area 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 6 of 40 · Inhaler days supply
M06. An inhaler contains 120 actuations. Directions: inhale 2 puffs by mouth twice daily. Assume none are wasted. What is the days supply?
- A. 30 days
- B. 60 days
- C. 15 days
- D. 120 days
Show answer and worked solution
Answer: A — 30 days.
2 puffs × 2 times = 4 puffs a day. 120 ÷ 4 = 30 days.
Why not the others: B counts only 2 puffs a day. C counts 8 a day. D treats each actuation as a day.
PTCB outline area 4.1, 4.2. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 7 of 40 · Insulin days supply
M07. A patient uses one 10 mL vial of U-100 insulin (100 units per mL): 20 units every morning and 16 units every evening. How many full days will the vial cover?
- A. 25 days
- B. 27 days
- C. 28 days
- D. 36 days
Show answer and worked solution
Answer: B — 27 days.
Total: 10 mL × 100 units/mL = 1,000 units. Daily use: 20 + 16 = 36 units. 1,000 ÷ 36 = 27.8, so the vial covers 27 full days and leaves 28 units, short of a full day's 36.
Why not the others: C rounds up to a day the patient can't complete. D is the daily dose, not days. A assumes 40 units a day.
The question asks for full days, so round down. That's the wording of this exercise, not a universal insurance billing rule.
PTCB outline area 4.1, 4.2, 1.7. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Questions 8–13: Conversions and Roman numerals
Question 8 of 40 · Household conversion
M08. A parent asks how much 2.5 mL is in teaspoons. Using 1 teaspoon = 5 mL, what is 2.5 mL?
- A. 1 teaspoon
- B. ¼ teaspoon
- C. 1 tablespoon
- D. ½ teaspoon
Show answer and worked solution
Answer: D — ½ teaspoon.
2.5 mL ÷ 5 mL per teaspoon = ½ teaspoon.
Why not the others: B is 1.25 mL. A is 5 mL. C is 15 mL.
ISMP lists tsp and tbsp as error-prone because they get mistaken for each other, and it recommends metric doses. In real practice the better answer for this parent is to measure 2.5 mL with an oral syringe.
PTCB outline area 4.1. Source: NIST, Metric Kitchen: Cooking Measurement Equivalencies; ISMP, List of Error-Prone Abbreviations, Symbols, and Dose Designations (2024).
Question 9 of 40 · Household to metric
M09. Directions: take 1 tablespoonful by mouth three times daily for 10 days. How many mL are needed? (1 tablespoon = 15 mL.)
- A. 150 mL
- B. 450 mL
- C. 300 mL
- D. 45 mL
Show answer and worked solution
Answer: B — 450 mL.
15 mL × 3 doses = 45 mL a day, and 45 mL × 10 days = 450 mL.
Why not the others: A uses teaspoons (5 mL). C uses twice-daily dosing. D is only one day.
PTCB outline area 4.1. Source: NIST, Metric Kitchen: Cooking Measurement Equivalencies.
Question 10 of 40 · Metric conversion
M10. Convert 0.25 mg to micrograms (mcg).
- A. 250 mcg
- B. 25 mcg
- C. 2,500 mcg
- D. 0.00025 mcg
Show answer and worked solution
Answer: A — 250 mcg.
1 mg = 1,000 mcg. Moving to a smaller unit makes the number bigger: 0.25 × 1,000 = 250 mcg.
Why not the others: B and C are off by a factor of 10, exactly the size of a misplaced decimal. D divides when it should multiply.
PTCB outline area 4.1. Source: NIST, Metric (SI) Prefixes.
Question 11 of 40 · Weight conversion
M11. A patient weighs 154 lb. What is the weight in kilograms? (Use 1 kg = 2.2 lb.)
- A. 339 kg
- B. 77 kg
- C. 70 kg
- D. 15.4 kg
Show answer and worked solution
Answer: C — 70 kg.
154 ÷ 2.2 = 70 kg. A kilogram is heavier than a pound, so the kilogram number has to be smaller.
Why not the others: A multiplies by 2.2. B divides by 2. D divides by 10.
PTCB outline area 4.1. Source: NIST, Metric Kitchen: Cooking Measurement Equivalencies.
Question 12 of 40 · Roman numerals
M12. A prescription quantity is written "Disp: #XLV." How many units should be dispensed?
- A. 55
- B. 65
- C. 40
- D. 45
Show answer and worked solution
Answer: D — 45.
XL = 50 − 10 = 40, because a smaller numeral before a larger one is subtracted. V = 5. 40 + 5 = 45.
Why not the others: B reads XL as 60 by adding instead of subtracting. A misreads the order. C ignores the V.
PTCB names Roman numerals in outline area 4.1. ISMP advises against Roman numerals for doses, but you'll still see them in quantities.
PTCB outline area 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026); ISMP, List of Error-Prone Abbreviations, Symbols, and Dose Designations (2024).
Question 13 of 40 · Microgram dose from a mg/mL solution
M13. An order calls for 600 mcg. The solution on hand is 3 mg/mL. How many mL contain 600 mcg?
- A. 0.2 mL
- B. 2 mL
- C. 0.02 mL
- D. 200 mL
Show answer and worked solution
Answer: A — 0.2 mL.
Match the units first: 600 mcg ÷ 1,000 = 0.6 mg. Then 0.6 mg ÷ 3 mg/mL = 0.2 mL.
Why not the others: B and C are 10-fold errors. D treats 600 mcg as if it were 600 mg.
PTCB outline area 4.1, 1.4. Source: NIST, Metric (SI) Prefixes.
Questions 14–19: Dose calculations
Question 14 of 40 · Tablets per dose
M14. An order calls for a 750 mg dose. The pharmacy stocks 250 mg tablets. How many tablets make one dose?
- A. 2
- B. 4
- C. 3
- D. 1.5
Show answer and worked solution
Answer: C — 3 tablets.
Dose ÷ tablet strength = 750 ÷ 250 = 3 tablets.
Why not the others: D would be right for 500 mg tablets. A gives 500 mg and B gives 1,000 mg.
PTCB outline area 1.4, 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 15 of 40 · Oral liquid dose
M15. Amoxicillin 300 mg is ordered. The suspension on hand is 250 mg/5 mL. How many mL per dose?
- A. 5 mL
- B. 6 mL
- C. 7.5 mL
- D. 3 mL
Show answer and worked solution
Answer: B — 6 mL.
Concentration: 250 mg ÷ 5 mL = 50 mg/mL. Volume: 300 mg ÷ 50 mg/mL = 6 mL. Proportion check: 250 mg : 5 mL = 300 mg : x, so x = (300 × 5) ÷ 250 = 6.
Why not the others: A gives only 250 mg. C gives 375 mg. D gives 150 mg.
PTCB outline area 1.4, 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 16 of 40 · Weight-based dose
M16. A child weighs 44 lb. The prescriber orders 15 mg/kg per dose. How many mg per dose? (Use 1 kg = 2.2 lb.)
- A. 660 mg
- B. 150 mg
- C. 30 mg
- D. 300 mg
Show answer and worked solution
Answer: D — 300 mg.
Convert first: 44 lb ÷ 2.2 = 20 kg. Then 20 kg × 15 mg/kg = 300 mg.
Why not the others: A uses pounds as if they were kilograms (44 × 15), a 2.2-fold overdose and the classic weight-based error. B would fit a 10 kg child. C is 2 × 15, a slip that drops the weight entirely.
PTCB outline area 1.4, 4.1. Source: NIST, Metric Kitchen: Cooking Measurement Equivalencies.
Question 17 of 40 · Weight-based dose to volume
M17. A child weighs 22 lb. Ibuprofen is ordered at 10 mg/kg per dose. The suspension is 100 mg/5 mL. How many mL per dose?
- A. 5 mL
- B. 10 mL
- C. 11 mL
- D. 2.5 mL
Show answer and worked solution
Answer: A — 5 mL.
22 lb ÷ 2.2 = 10 kg. Dose: 10 kg × 10 mg/kg = 100 mg. Concentration: 100 mg ÷ 5 mL = 20 mg/mL. Volume: 100 ÷ 20 = 5 mL.
Why not the others: C skips the pound-to-kilogram step (220 mg). B doubles the dose. D halves it.
PTCB outline area 1.4, 4.1. Source: NIST, Metric Kitchen: Cooking Measurement Equivalencies.
Question 18 of 40 · Divided daily dose
M18. A 25 kg child is prescribed amoxicillin 40 mg/kg/day divided every 12 hours. The suspension is 400 mg/5 mL. How many mL per dose?
- A. 12.5 mL
- B. 3.125 mL
- C. 6.25 mL
- D. 5 mL
Show answer and worked solution
Answer: C — 6.25 mL.
Daily: 25 kg × 40 mg/kg = 1,000 mg a day. Every 12 hours means 2 doses, so 500 mg per dose. Concentration: 400 mg ÷ 5 mL = 80 mg/mL. Volume: 500 ÷ 80 = 6.25 mL.
Why not the others: A gives the whole day's amount in one dose instead of dividing it into the two q12h doses stated in the order. B splits the daily amount into four doses. D is 400 mg.
PTCB outline area 1.4, 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 19 of 40 · Grams to a liquid dose
M19. An order calls for 0.375 g. The liquid on hand contains 125 mg per 5 mL. What volume contains the ordered amount?
- A. 1.5 mL
- B. 15 mL
- C. 5 mL
- D. 150 mL
Show answer and worked solution
Answer: B — 15 mL.
Match the units: 0.375 g × 1,000 = 375 mg. Then 375 mg × 5 mL ÷ 125 mg = 15 mL.
Why not the others: A gives 37.5 mg, a tenth of the order. C gives only 125 mg. D gives 3,750 mg, ten times the order.
PTCB outline area 1.4, 4.1. Source: NIST, Metric (SI) Prefixes.
Questions 20–25: Concentration, percent, and ratio strength
Question 20 of 40 · Percent strength (w/v)
M20. How many grams of dextrose are in 500 mL of D5W (dextrose 5% in water)?
- A. 2.5 g
- B. 5 g
- C. 250 g
- D. 25 g
Show answer and worked solution
Answer: D — 25 g.
Percent weight-in-volume (w/v) means grams per 100 mL. 5% = 5 g per 100 mL. 500 mL holds five 100 mL portions, so 5 g × 5 = 25 g.
Why not the others: B is the amount in 100 mL. A reads 5% as 5 g per liter. C is ten times too high.
PTCB outline area 4.1. Source: FDA, Strength Conversion in Drug Listing (w/v, w/w, v/v).
Question 21 of 40 · Percent to milligrams
M21. How many mg of lidocaine are in 10 mL of a 2% lidocaine solution?
- A. 200 mg
- B. 20 mg
- C. 2,000 mg
- D. 2 mg
Show answer and worked solution
Answer: A — 200 mg.
2% w/v = 2 g per 100 mL = 2,000 mg per 100 mL = 20 mg/mL. Then 20 mg/mL × 10 mL = 200 mg. Shortcut for w/v: % × 10 = mg/mL.
Why not the others: B is the amount in 1 mL. C is the amount in 100 mL. D is off by a factor of 100.
PTCB outline area 4.1. Source: FDA, Strength Conversion in Drug Listing (w/v, w/w, v/v).
Question 22 of 40 · Ratio strength
M22. An epinephrine vial uses the older ratio strength label 1:1,000. What is its concentration in mg/mL?
- A. 0.1 mg/mL
- B. 1 mg/mL
- C. 10 mg/mL
- D. 0.01 mg/mL
Show answer and worked solution
Answer: B — 1 mg/mL.
1:1,000 means 1 g in 1,000 mL = 1,000 mg in 1,000 mL = 1 mg/mL.
Why not the others: A is 1:10,000. D is 1:100,000. C would be 1:100.
ISMP lists ratio expressions for single-ingredient injectables as error-prone and recommends writing strength as quantity per volume, which is the conversion you just did.
PTCB outline area 4.1, 3.2. Source: ISMP, List of Error-Prone Abbreviations, Symbols, and Dose Designations (2024).
Question 23 of 40 · Reconstitution
M23. A vial contains 1 g of Drug Y as a powder. The label says: add 9.3 mL of sterile water to make a final volume of 10 mL. The order is 250 mg. How many mL should be drawn up?
- A. 25 mL
- B. 0.25 mL
- C. 2.5 mL
- D. 2.3 mL
Show answer and worked solution
Answer: C — 2.5 mL.
The powder takes up space, so the final volume (10 mL) sets the concentration, not the 9.3 mL you add. 1,000 mg ÷ 10 mL = 100 mg/mL, and 250 mg ÷ 100 mg/mL = 2.5 mL.
Why not the others: D uses 9.3 mL as the volume (250 ÷ 107.5 ≈ 2.3). A and B are 10-fold errors.
Drug Y is fictional. For a real product, use the concentration its label gives after reconstitution.
PTCB outline area 1.7, 4.1. Source: Open RN, Nursing Skills 5.10: Reconstituted Medication.
Question 24 of 40 · Milliequivalents
M24. Potassium chloride is available as 2 mEq/mL. An order calls for 40 mEq. How many mL?
- A. 80 mL
- B. 2 mL
- C. 10 mL
- D. 20 mL
Show answer and worked solution
Answer: D — 20 mL.
Amount ÷ concentration = 40 mEq ÷ 2 mEq/mL = 20 mL.
Why not the others: A multiplies instead of dividing. C assumes 4 mEq/mL. B is the concentration number, not a volume.
PTCB outline area 1.4, 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 25 of 40 · Percent strength (w/w)
M25. A 30 g tube of hydrocortisone cream is labeled 2.5%. For a cream, percent means weight-in-weight (w/w): grams of drug per 100 g of cream. How many grams of hydrocortisone are in the tube?
- A. 7.5 g
- B. 0.75 g
- C. 75 g
- D. 0.075 g
Show answer and worked solution
Answer: B — 0.75 g.
30 g × 2.5 g ÷ 100 g = 0.75 g (750 mg).
Why not the others: A and D are 10-fold errors. C forgets to divide by 100 and would weigh more than the whole tube.
PTCB outline area 4.1. Source: FDA, Strength Conversion in Drug Listing (w/v, w/w, v/v).
Questions 26–28: Dilutions
Question 26 of 40 · Dilution: stock needed
M26. You need 200 mL (final volume) of a 5% solution. You have a 20% stock solution. How many mL of stock do you need?
- A. 50 mL
- B. 40 mL
- C. 80 mL
- D. 150 mL
Show answer and worked solution
Answer: A — 50 mL.
C₁ × V₁ = C₂ × V₂, so 20% × V₁ = 5% × 200 mL, and V₁ = 1,000 ÷ 20 = 50 mL of stock, brought up to 200 mL with diluent.
Why not the others: D is the diluent, not the stock. B and C come from mismatched ratios.
PTCB outline area 4.1. Source: OpenStax, Chemistry 2e, 3.3 (Dilution of Solutions).
Question 27 of 40 · Dilution: diluent to add
M27. You have 100 mL of a 10% solution and must dilute it to 4%. Assume the volumes add together exactly. How much diluent should you add?
- A. 250 mL
- B. 40 mL
- C. 60 mL
- D. 150 mL
Show answer and worked solution
Answer: D — 150 mL.
Final volume: (10% × 100 mL) ÷ 4% = 250 mL. You already have 100 mL, so add 250 − 100 = 150 mL.
Why not the others: A is the final volume, the most common trap on "how much do I add" questions. B and C don't come from the equation (C is 100 − 40).
The subtraction works here because the question tells you volumes add exactly. Some real mixtures don't, which is why preparation directions often say to add diluent up to a final volume.
PTCB outline area 4.1. Source: OpenStax, Chemistry 2e, 3.3 (Dilution of Solutions).
Question 28 of 40 · Concentration after dilution
M28. 2 mL of a 50 mg/mL solution is diluted with sterile water to a total volume of 10 mL. What is the new concentration?
- A. 25 mg/mL
- B. 5 mg/mL
- C. 10 mg/mL
- D. 100 mg/mL
Show answer and worked solution
Answer: C — 10 mg/mL.
Drug amount: 2 mL × 50 mg/mL = 100 mg. Spread through 10 mL: 100 ÷ 10 = 10 mg/mL. Dilution changes the volume, never the amount of drug.
Why not the others: D is the drug amount in mg, not a concentration. A and B divide by the wrong volume.
PTCB outline area 4.1, 4.2. Source: OpenStax, Chemistry 2e, 3.3 (Dilution of Solutions).
Questions 29–32: IV rates and infusion time
Question 29 of 40 · IV rate (mL/hour)
M29. 1,000 mL of IV fluid is to run over 8 hours. What is the rate in mL per hour?
- A. 125 mL/hour
- B. 80 mL/hour
- C. 8 mL/hour
- D. 250 mL/hour
Show answer and worked solution
Answer: A — 125 mL/hour.
Volume ÷ time = 1,000 mL ÷ 8 hours = 125 mL/hour. Check: 125 × 8 = 1,000.
Why not the others: D would finish in 4 hours. B and C don't match the order.
PTCB outline area 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 30 of 40 · Drip rate (drops/minute)
M30. 1,000 mL is to run over 8 hours using tubing with a drop factor of 15 drops/mL. What is the rate in drops per minute, rounded to the nearest whole drop?
- A. 125 drops/minute
- B. 31 drops/minute
- C. 8 drops/minute
- D. 21 drops/minute
Show answer and worked solution
Answer: B — 31 drops/minute.
Drops/minute = (volume × drop factor) ÷ minutes = (1,000 × 15) ÷ (8 × 60) = 15,000 ÷ 480 = 31.25, which rounds to 31 drops/minute.
Why not the others: A is the mL/hour rate. D uses a 10 drops/mL set. C is the number of hours.
PTCB outline area 4.1, 4.2. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 31 of 40 · Infusion end time
M31. A 500 mL bag is started at 0800 and runs at 200 mL/hour. At what time will it finish?
- A. 1050
- B. 1025
- C. 1300
- D. 1030
Show answer and worked solution
Answer: D — 1030.
Time = volume ÷ rate = 500 ÷ 200 = 2.5 hours. Half an hour is 30 minutes, so 0800 + 2 hours 30 minutes = 1030 (10:30 a.m.).
Why not the others: A reads 2.5 hours as 2 hours 50 minutes. B reads it as 2 hours 25 minutes. C assumes 100 mL/hour.
PTCB outline area 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 32 of 40 · Units per hour to mL per hour
M32. A bag contains heparin 25,000 units in 500 mL. The order is 1,000 units per hour. What rate in mL per hour delivers that dose?
- A. 50 mL/hour
- B. 0.05 mL/hour
- C. 20 mL/hour
- D. 40 mL/hour
Show answer and worked solution
Answer: C — 20 mL/hour.
Concentration: 25,000 units ÷ 500 mL = 50 units/mL. Rate: 1,000 units/hour ÷ 50 units/mL = 20 mL/hour. Check: 20 mL × 50 units/mL = 1,000 units.
Why not the others: A is the concentration in units per mL. B divides the wrong way. D uses 25 units/mL, as if the bag were 1,000 mL.
Write "units," never "U." ISMP notes that "U" can be misread as 0 or 4.
PTCB outline area 4.1, 3.2. Source: ISMP, List of Error-Prone Abbreviations, Symbols, and Dose Designations (2024).
Questions 33–35: Federal limits and stability math
Question 33 of 40 · Controlled-substance refill math
M33. A Schedule IV prescription reads: lorazepam 0.5 mg, take 1 tablet by mouth bid, #30, refills: 5. Assume every fill happens within six months of the date it was issued. Under the federal refill limit, what is the most tablets that can be dispensed on this prescription?
- A. 180
- B. 150
- C. 210
- D. 30
Show answer and worked solution
Answer: A — 180 tablets.
Federal rule for Schedule III and IV: no more than 5 refills, and no fill or refill more than 6 months after the prescription was issued. Original fill + 5 refills = 6 fills × 30 tablets = 180 tablets. Under the question's assumption that every fill occurs within six months, the federal refill-count limit is the binding limit.
Why not the others: B forgets the original fill. C counts a sixth refill the rule doesn't allow. D is one fill.
The federal rule is the floor. Your state may be stricter.
PTCB outline area 2.2. Source: eCFR, 21 CFR 1306.22 (refilling Schedule III-IV prescriptions).
Question 34 of 40 · Pseudoephedrine daily limit
M34. For this exercise, use 98 mg of pseudoephedrine base per 120 mg pseudoephedrine HCl tablet. Federal law limits retail sales to 3.6 g of pseudoephedrine base per purchaser per day. What is the most whole tablets one customer can buy in a day?
- A. 30
- B. 36
- C. 37
- D. 45
Show answer and worked solution
Answer: B — 36 tablets.
3.6 g = 3,600 mg. 3,600 ÷ 98 = 36.7. You can't go over the limit, so round down to 36 tablets. DEA's federal equivalency chart also lists 36 tablets for 120 mg pseudoephedrine HCl.
Why not the others: C rounds up and exceeds the limit. A divides by the salt weight (120 mg) instead of the base. D has no basis in the numbers.
PTCB outline area 2.4. Source: 21 U.S.C. § 830(d); DEA Diversion Control, CMEA retail transaction limits.
Question 35 of 40 · In-use stability
M35. The labeling in this scenario says an opened insulin vial must be discarded 28 days after first use. A patient starts a new 10 mL vial of U-100 insulin (100 units/mL) and uses 15 units a day. How many units are left to discard on day 28?
- A. 0 units
- B. 420 units
- C. 1,000 units
- D. 580 units
Show answer and worked solution
Answer: D — 580 units.
Vial: 10 × 100 = 1,000 units. Used in 28 days: 15 × 28 = 420 units. Left: 1,000 − 420 = 580 units. The vial expires before it runs out.
Why not the others: B is what was used. A assumes the vial empties first. C is the starting amount.
In-use periods vary by product. Always use the product's own labeling.
PTCB outline area 1.7, 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Questions 36–40: Error checks, NDC, and supplies
Question 36 of 40 · Catching a dose error
M36. Order: cephalexin 200 mg by mouth bid. Stock: cephalexin 250 mg/5 mL. The typed label reads "Give 40 mL twice daily." Which statement is correct?
- A. 40 mL is correct; the label can go to final check.
- B. The correct volume is 8 mL; the label is off by a factor of 5.
- C. The correct volume is 4 mL; the label shows a tenfold dose error and should be stopped for the pharmacist.
- D. The correct volume is 0.4 mL; the label is 100 times too high.
Show answer and worked solution
Answer: C — 4 mL, and the label has a tenfold error.
250 mg ÷ 5 mL = 50 mg/mL, and 200 mg ÷ 50 mg/mL = 4 mL. The label says 40 mL, ten times the dose. That's an incorrect-dose prescription error, and it goes to the pharmacist before anything else happens.
Why not the others: A accepts the error. B uses 25 mg/mL. D slips the decimal the other way.
PTCB outline area 3.5, 4.1. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 37 of 40 · Maximum daily dose check
M37. For this question only, assume Drug X's labeling sets a maximum of 40 mg per day. A prescription for Drug X 10 mg tablets reads: take 2 tablets by mouth tid. What should the technician conclude?
- A. The directions total 60 mg/day, above the stated maximum; flag it for the pharmacist.
- B. The directions total 20 mg/day, within the maximum; process it.
- C. The directions total 30 mg/day, within the maximum; process it.
- D. The directions total 60 mg/day; change the directions to 40 mg/day and process it.
Show answer and worked solution
Answer: A — 60 mg/day; flag it for the pharmacist.
2 tablets × 10 mg × 3 times a day = 60 mg/day, which is more than 40 mg/day. A dose over the maximum is an issue that needs pharmacist intervention.
Why not the others: B counts one dose. C counts one tablet per dose. D gets the math right and the action wrong: a technician doesn't rewrite a prescriber's directions.
PTCB outline area 3.3. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Question 38 of 40 · Leading zero
M38. An order for 0.5 mg is written as ".5 mg," and the decimal point is missed, so it's read as 5 mg. How many times the intended dose would the patient get?
- A. 2 times
- B. 5 times
- C. 50 times
- D. 10 times
Show answer and worked solution
Answer: D — 10 times.
5 mg ÷ 0.5 mg = 10. That's why ISMP says to always use a leading zero (0.5 mg) and never a trailing zero (write 1 mg, not 1.0 mg, which can be read as 10 mg).
Why not the others: A, B, and C don't match the ratio between 5 mg and 0.5 mg.
PTCB outline area 3.2, 3.5. Source: ISMP, List of Error-Prone Abbreviations, Symbols, and Dose Designations (2024).
Question 39 of 40 · NDC format
M39. A package is labeled NDC 12345-678-90 (a 5-3-2 format). Billing systems use an 11-digit 5-4-2 format. Which is the correct 11-digit version?
- A. 01234-5678-90
- B. 12345-0678-90
- C. 12345-6780-90
- D. 12345-678-090
Show answer and worked solution
Answer: B — 12345-0678-90.
To reach 5-4-2, add a leading zero to whichever segment is short. Here the middle (product) segment has 3 digits, so it becomes 0678.
Why not the others: A pads the first segment, which is the fix for a 4-4-2 code. C adds a trailing zero, which changes the number. D pads the last segment to 3 digits.
As of September 2026, FDA still assigns 10-digit NDCs. A uniform 12-digit FDA-assigned NDC format takes effect on March 7, 2033, and FDA says that change does not alter the HIPAA standard 11-digit format used for reimbursement.
PTCB outline area 4.3. Source: FDA, National Drug Code Format; California DWC, NDC 10-to-11-digit conversion chart.
Question 40 of 40 · Insulin syringe volume
M40. A patient needs 25 units of U-100 insulin (100 units/mL). How many mL is that?
- A. 2.5 mL
- B. 0.025 mL
- C. 0.25 mL
- D. 25 mL
Show answer and worked solution
Answer: C — 0.25 mL.
25 units ÷ 100 units/mL = 0.25 mL. You'd read unit markings directly on an insulin syringe, but knowing the volume tells you which syringe size fits.
Why not the others: A and B are 10-fold errors. D confuses units with mL.
PTCB outline area 4.2. Source: PTCB, PTCE Content Outline (effective Jan 6, 2026).
Check your work
Answer key: 1 B · 2 D · 3 A · 4 C · 5 C · 6 A · 7 B · 8 D · 9 B · 10 A · 11 C · 12 D · 13 A · 14 C · 15 B · 16 D · 17 A · 18 C · 19 B · 20 D · 21 A · 22 B · 23 C · 24 D · 25 B · 26 A · 27 D · 28 C · 29 A · 30 B · 31 D · 32 C · 33 A · 34 B · 35 D · 36 C · 37 A · 38 D · 39 B · 40 C
Count your first-try answers only. If you opened a solution before choosing, count that question as a study question, not a correct answer. Your total is how you did on these 40 original questions. It isn't a PTCE scaled score, and it can't predict whether you'll pass.
Then look at where your misses cluster. Some groups have only three or four questions, so treat a group result as a pointer to what to rework first, not a measurement of your ability.
| If you missed questions in… | Review | What to write down before you calculate again |
|---|---|---|
| Sig codes, quantity, and days supply | 1–7 | Amount per dose × doses per day. Then total ÷ daily use. |
| Conversions and Roman numerals | 8–13 | Starting unit, target unit, and the conversion factor. |
| Dose calculations | 14–19 | Whether the order is per dose or per day, and the weight in kg. |
| Concentration, percent, and ratio strength | 20–25 | What the denominator is: per mL, per 100 mL, or per 100 g. |
| Dilutions | 26–28 | Stock volume, diluent volume, and final volume as three separate numbers. |
| IV rates and infusion time | 29–32 | The unit the question wants, then a reverse check. |
| Federal limits and stability math | 33–35 | The rule's limit, and whether you must round down to stay under it. |
| Error checks, NDC, and supplies | 36–40 | The correct number first, then what the difference means. |
Rework every missed question from a blank page before you look at the solution again, and say the setup out loud in words. Most pharmacy math misses are setup errors, and the calculator can't fix those. If your score jumps on a second pass, some of that is memory of these exact questions. The explanations matter more than the letter.
Once you're accurate, add time. The PTCE gives up to 110 minutes for 90 questions, about 73 seconds each (our arithmetic). At that pace, this set takes about 49 minutes.
PTCB math formulas and conversions
Start with the unit you want. Set up the numbers so the units you don't want cancel out, then calculate and ask whether the answer makes sense. Two mix-ups cause a lot of misses here: per day versus per dose (question 18) and final volume versus volume added (questions 23 and 27).
| You need | Use |
|---|---|
| Days supply | quantity ÷ amount used per day |
| Quantity to dispense | amount per dose × doses per day × days |
| Volume for a dose | dose ÷ concentration (for example, mg ÷ mg/mL) |
| Volume from a "per 5 mL" label | dose × 5 mL ÷ mg in 5 mL |
| Weight-based dose | weight in kg × mg/kg (convert pounds first) |
| Divided daily dose | (mg/kg/day × kg) ÷ doses per day |
| Dilution | C₁ × V₁ = C₂ × V₂, where V₂ is the final volume |
| Concentration | total drug ÷ final volume |
| IV rate | mL/hour = volume ÷ hours |
| Drip rate | drops/minute = (mL × drop factor) ÷ minutes |
| Infusion time | hours = volume ÷ rate; decimal hours × 60 = minutes |
| Percent w/v | grams per 100 mL (so % × 10 = mg/mL) |
| Percent w/w | grams per 100 g |
| Ratio strength | 1:1,000 = 1 g per 1,000 mL = 1 mg/mL |
| Conversion | Value |
|---|---|
| 1 g | 1,000 mg |
| 1 mg | 1,000 mcg |
| 1 L | 1,000 mL |
| 1 kg | 2.2 lb |
| 1 lb | about 454 g |
| 1 teaspoon | 5 mL |
| 1 tablespoon | 15 mL |
| 1 fluid ounce | 30 mL |
| 16 fluid ounces (1 pint) | 480 mL |
The metric steps come from the NIST metric prefix table, and the household and weight figures are the standard approximations NIST publishes. Percent definitions follow FDA's strength-conversion page, and the dilution equation is explained in OpenStax Chemistry 2e, section 3.3.
Rounding follows the question. Round at the end, not in the middle. "Full days" means round down (question 7). "Nearest whole drop" means ordinary rounding (question 30). A legal limit means round down so you stay under it (question 34).
When you write a dose, use metric units, a leading zero, and no trailing zero: 0.5 mg, not .5 mg; 1 mg, not 1.0 mg (ISMP).
What math is on the current PTCE?
PTCB doesn't publish a number or percentage of math questions. Its current content outline marks 9 of its 24 knowledge areas as involving calculation-based knowledge: 1.4, 1.7, 2.2, 2.4, 3.3, 3.5, 4.1, 4.2, and 4.3. Those areas sit in all four exam domains, not just Order Entry and Processing. That's why this set includes controlled-substance refill math, the pseudoephedrine limit, drug stability, and error checks, not only dosing.
Area 4.1 names the core calculation work: formulas, ratios, proportions, conversions, Sig codes (including Roman numerals), and the symbols used for days supply, quantity, dose, concentration, and dilutions.
Alligation isn't part of the current outline. When the new outline took effect in January 2026, PTCB removed "alligations" along with its nonsterile compounding knowledge areas (PTCB job analysis notice). That's why there are no alligation questions here. It isn't a promise that no mixing arithmetic can ever appear, but study material that still treats alligation as core exam math is teaching the older outline.
This set isn't a full-length exam. The PTCE has 90 multiple-choice questions, 80 scored and 10 unscored, with four answer choices and one correct or best answer each (PTCB CPhT Program guidebook; PTCB At-a-Glance). These questions use the same four-choice format.
Can you use a calculator on the PTCB exam?
Yes. A calculator is built into the exam, and you can't bring your own. If you ask for a hand-held calculator and the test center has one, you may use it, but availability isn't guaranteed (PTCB calculator policy).
Practice with an on-screen calculator before test day, and write the setup and units before you type anything. A calculator can't tell a daily amount from a single dose for you.
Sources and scope
For everything else on the exam, including the 2026 outline, fees, retakes, and a study planner, see the Castleport PTCB exam hub. Taking the NHA exam instead? That's a different test from a different organization, covered in the ExCPT hub.
By the Castleport Test Prep Editorial Team. Last verified: September 24, 2026. That date covers the PTCE content outline and 2026 changes, the exam format, the calculator policy, and the regulations, standards, and references cited in the answers.
What we checked:
- PTCB: PTCE Content Outline (v1.4, effective January 6, 2026); job analysis notice; CPhT Program guidebook; At-a-Glance: CPhT Exam; Calculators.
- Federal rules: 21 CFR 1306.22 (Schedule III–IV refills); 21 U.S.C. § 830(d) and DEA CMEA retail transaction limits (pseudoephedrine); FDA National Drug Code Format; FDA Strength Conversion in Drug Listing.
- Safety and measurement: ISMP error-prone abbreviations list (2024); NIST metric prefixes; NIST cooking measurement equivalencies; California DWC NDC conversion chart.
- Calculation methods: OpenStax Chemistry 2e, 3.3; Open RN, Reconstituted Medication.
- Every numeric answer was recomputed from the values in its question, and every question was checked for a single defensible answer.
The questions are original. We don't claim a count of math questions on the PTCE, where any question falls on a real exam form, or what a score here predicts. Source checking and arithmetic checks aren't a pharmacist's clinical review. Found an error? Report it. Corrections are dated and public.
Castleport Test Prep is an independent exam prep publisher and is not affiliated with, endorsed by, or approved by the Pharmacy Technician Certification Board (PTCB). Exam and credential names are used to identify the exams discussed; trademarks belong to their respective owners. All 40 questions are original, unofficial practice items, not real, recalled, or retired PTCE questions. No passing score, certification, or licensure is guaranteed.